en translated into French: in
the mean time he congratulates the author upon his victory over a problem
so long held insoluble. All this is seriously published as a rate in aid of
demonstration. If these royal compliments cannot make the circumference of
a circle about 2 per cent. larger than geometry will have it --which is all
that is wanted--no wonder that thrones are shaky.

I am informed that the legend of St. Vitus is given by Ribadeneira[132] in
his lives of Saints, and that Baronius,[133] in {63} his _Martyrologium
Romanum_, refers to several authors who have written concerning him. There
is an account in Mrs. Jameson's[134] _History of Sacred and Legendary Art_
(ed. of 1863, p. 544). But it seems that St. Vitus is the patron saint of
_all_ dances; so that I was not so far wrong in making him the protector of
the cyclometers. Why he is represented with a cock is a disputed point,
which is now made clear: next after _gallus gallinaceus_[135] himself,
there is no crower like the circle-squarer.

CELEBRATED APPROXIMATIONS OF [pi].

The following is an extract from the _English Cyclopaedia_, Art. TABLES:

"1853. William Shanks,[136] _Contributions to Mathematics, comprising
chiefly the Rectification of the Circle to 607 Places of Tables_, London,
1853. (QUADRATURE OF THE CIRCLE.) Here is a _table_, because it tabulates
the results of the subordinate steps of this enormous calculation as far as
527 decimals: the remainder being added as results only during the
printing. For instance, one step is the calculation of the reciprocal of
601.5^{601}; and the result is given. The number of pages required to
describe these results is 87. Mr. Shanks has also thrown off, as chips or
splinters, the values of the base of Napier's logarithms, and of its
logarithms of 2, 3, 5, 10, to 137 decimals; and the value of the modulus
.4342 ... to 136 decimals: with the 13th, 25th, 37th ... up to the 721st
powers of 2. These tremendous stretches of calculation--at least we so call
them in our day--are useful in several respects; they prove more than {64}
the capacity of this or that computer for labor and accuracy; they show
that there is in the community an increase of skill and courage. We say in
the community: we fully believe that the unequalled turnip which every now
and then appears in the newspapers is a sufficient presumption that the
average turnip is growing bigger, and the whole crop heavier. All who know
the history of th